from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
A						=			numpy.array([0, 0])
A						=			numpy.array([0.5, 0.8_66_02_54])
A						=			numpy.array([1, 0])
A						=			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def 	lowerCamelCase					(	UpperCamelCase     :				list[numpy.ndarray]			,       UpperCamelCase     :				int							)   ->    list[numpy.ndarray]:
		_lowerCamelCase				   =  initial_vectors
		for _ in range(UpperCamelCase							):
				_lowerCamelCase				   =  iteration_step(UpperCamelCase							)
		return vectors


def 	lowerCamelCase					(	UpperCamelCase     :				list[numpy.ndarray]							)   ->    list[numpy.ndarray]:
		_lowerCamelCase				   =  []
		for i, start_vector in enumerate(vectors[:-1]							):
				_lowerCamelCase				   =  vectors[i + 1]
				new_vectors.append(UpperCamelCase							)
				_lowerCamelCase				   =  end_vector - start_vector
				new_vectors.append(start_vector + difference_vector / 3							)
				new_vectors.append(
				    start_vector + difference_vector / 3 + rotate(difference_vector / 3			,       60							)							)
				new_vectors.append(start_vector + difference_vector * 2 / 3							)
		new_vectors.append(vectors[-1]							)
		return new_vectors


def 	lowerCamelCase					(	UpperCamelCase     :				numpy.ndarray			,       UpperCamelCase     :				float							)   ->    numpy.ndarray:
		_lowerCamelCase				   =  numpy.radians(UpperCamelCase							)
		_lowerCamelCase   ,							_lowerCamelCase				   =  numpy.cos(UpperCamelCase							), numpy.sin(UpperCamelCase							)
		_lowerCamelCase				   =  numpy.array(((c, -s), (s, c))							)
		return numpy.dot(UpperCamelCase			,       UpperCamelCase							)


def 	lowerCamelCase					(	UpperCamelCase     :				list[numpy.ndarray]							)   ->    None:
		_lowerCamelCase				   =  plt.gca()
		axes.set_aspect('equal'							)

		# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
		# y-coordinates as inputs, which are constructed from the vector-list using
		# zip()
		_lowerCamelCase   ,							_lowerCamelCase				   =  zip(*UpperCamelCase							)
		plt.plot(UpperCamelCase			,       UpperCamelCase							)
		plt.show()


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				A						=			iterate(INITIAL_VECTORS, 5)
				plot(processed_vectors)
A						=			'\n# Transformers installation\n! pip install transformers datasets\n# To install from source instead of the last release, comment the command above and uncomment the following one.\n# ! pip install git+https://github.com/huggingface/transformers.git\n'

A						=			[{'type': 'code', 'content': INSTALL_CONTENT}]
A						=			{
    '{processor_class}': 'FakeProcessorClass',
    '{model_class}': 'FakeModelClass',
    '{object_class}': 'FakeObjectClass',
}